The last term in equation (REF ) can be handled using [1]} from which we get that there exists an absolute constant \(K>0\)  such that
\(\left\Vert  \max _{1\le i\le n} \Vert Y_i\Vert  \right\Vert _{\psi _1}\le K\log (n) \left\Vert Y_i \right\Vert _{\psi _1}.\) 
